Local subdivision process with Doo-Sabin subdivision surfaces

One problem in subdivision surfaces is that the number of meshes grows quickly after every subdivision step, and a surface with a huge number of meshes is difficult to manipulate. In this paper, an adaptive process for carrying out local subdivision with a Doo-Sabin recursive subdivision surface is presented. With this process, we can create Doo-Sabin surfaces that are more densely subdivided in areas of higher curvature or in special areas decided by users. The Doo-Sabin surfaces are constructed using fewer meshes compared to the original Doo-Sabin method.

[1]  Charles T. Loop,et al.  Smooth Subdivision Surfaces Based on Triangles , 1987 .

[2]  Kunio Kondo,et al.  Adaptive Refinements in Subdivision Surfaces? , 1999, Eurographics.

[3]  E. Catmull,et al.  Recursively generated B-spline surfaces on arbitrary topological meshes , 1978 .

[4]  Greg Turk,et al.  Re-tiling polygonal surfaces , 1992, SIGGRAPH.

[5]  Luiz Velho,et al.  Variable Resolution 4‐k Meshes: Concepts and Applications , 2000, Comput. Graph. Forum.

[6]  Ahmad H. Nasri,et al.  Polyhedral subdivision methods for free-form surfaces , 1987, TOGS.

[7]  Tony DeRose,et al.  Efficient, fair interpolation using Catmull-Clark surfaces , 1993, SIGGRAPH.

[8]  Tony DeRose,et al.  Multiresolution analysis for surfaces of arbitrary topological type , 1997, TOGS.

[9]  Peter Schröder,et al.  Interpolating Subdivision for meshes with arbitrary topology , 1996, SIGGRAPH.

[10]  Peter Schröder,et al.  Interactive multiresolution mesh editing , 1997, SIGGRAPH.

[11]  G. Farin.  Designing C1 surfaces consisting of triangular cubic patches , 1982 .

[12]  George Merrill Chaikin,et al.  An algorithm for high-speed curve generation , 1974, Comput. Graph. Image Process..

[13]  Malcolm A. Sabin,et al.  Non-uniform recursive subdivision surfaces , 1998, SIGGRAPH.

[14]  Tony DeRose,et al.  Mesh optimization , 1993, SIGGRAPH.

[15]  Leif Kobbelt,et al.  Interpolatory Subdivision on Open Quadrilateral Nets with Arbitrary Topology , 1996, Comput. Graph. Forum.

[16]  M. Sabin,et al.  Behaviour of recursive division surfaces near extraordinary points , 1978 .

[17]  N. Dyn,et al.  A butterfly subdivision scheme for surface interpolation with tension control , 1990, TOGS.

[18]  Heinrich Müller,et al.  Adaptive subdivision curves and surfaces , 1998, Proceedings. Computer Graphics International (Cat. No.98EX149).